Fixed-Point Implementation of Discrete Hirschman Transform
Rajesh Thomas, Victor DeBrunner, Linda S. DeBrunner · 2018 52nd Asilomar Conference on Signals, Systems, and Computers · 2018
Digital Signal Processing (DSP) performs a very important role in various engineering applications, e.g. communications, control, imaging, audio, and radar. In many situations it is necessary to perform DSP with high accuracy using the least amount of hardware resources on fixed-point processors. This work looks into an approach to calculate the two-dimensional Discrete Hirschman Transform (DHT) and the inverse DHT using fixed-point processing hardware. The complex coefficients required for the transform are pre-calculated and stored as vectors. Special attention is given to minimizing errors due to scaling. The Mean Square Error (MSE) for 256 × 256 images is -37 dB when the number of sampling points is 128. This compares to an MSE of -34 dB for the DFT under the same constraints. The error gets proportionally lower when the number of sampling points chosen is less than 128.